Term Rewriting System R:

   [x]
   app(app(f, x), app(g, x)) -> app(app(f, 1), app(g, x))
   app(g, 1) -> app(g, 0)

Innermost Termination of R to be shown.


R contains the following Dependency Pairs: 


   APP(g, 1) -> APP(g, 0)
   APP(app(f, x), app(g, x)) -> APP(app(f, 1), app(g, x))
   APP(app(f, x), app(g, x)) -> APP(f, 1)

Furthermore, R contains one SCC.


SCC1:

APP(app(f, x), app(g, x)) -> APP(app(f, 1), app(g, x))

On this Scc, a Narrowing SCC transformation can be performed.
 
As a result of transforming the rule 

   APP(app(f, x), app(g, x)) -> APP(app(f, 1), app(g, x))
no new Dependency Pairs
are created.

none
The transformation is resulting in no subcycles.




Innermost Termination of R successfully shown.


Duration: 0.395 seconds.